The Study Of Virtual Element Method In Self-consistent Field Theory

Block copolymers,as a kind of important soft materials,can self-assemble to form various ordered microphase structures which are important in industrial applications.The self-consistent field theory is one of the most successful tools to study the self-assembly and thermodynamic stability of block polymer systems,which is favored by many researchers.The finite difference method,finite element method,spectral method and other numerical methods are used to study the selfconsistent field theory.Due to the accuracy and applicability of these numerical methods are limited,we take a flexible diblock copolymer system as an example,use the high order adaptive virtual element method to simulate the self-consistent field theory model on arbitrary domains.The virtual element method is very flexible in handling rather general polygonal elements and naturally treats the handing nodes,which is more suitable to discrete the model defined on complex geometric domain.In the direction of contour,we use spectral deferred correction method to discretize,it can efficiently improve the approximation order of contour derivative.The combination of these two methods makes our calculation more efficient and accurate.In addition,an adaptive method equipped with a new marking strategy is developed to effectively solve the self-consistent field model,which can achieve the desired accuracy with less computational cost.Results indicate that our approaches can efficiently produce high-accuracy numerical results.